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Mathematics
OpenStudy (anonymous):

f(x)=x^2. g(x)=x-3 a. Find gf(x) b. Fing g^-1 (x) c. Solve the equation gf(x)= g^-1 (x)

OpenStudy (anonymous):

PLEEEEAAAAAAAAAASEEEEEEEE HELP!!!!!!!!!!!!!

OpenStudy (anonymous):

does this mean \[f\circ g(x)\]?

OpenStudy (anonymous):

i.e. \[f(g(x))\]

OpenStudy (anonymous):

oops sorry it is \[g(f(x))\] ok first step replace the generic f by the specific one, get \[g(x^2)\] then evaluate g at x^2 get \[g(x^2)=x^2-3\]

OpenStudy (anonymous):

\[g(x)=x-3\] says to subtract 3, so \[g^{-1}(x)=x+3\] says to add 3. does the opposite action

OpenStudy (anonymous):

and finally \[g(f(x))=g^{-1}(x)\] means \[x^2-3=x+3\] making \[x^2-x-6=0\] \[(x+2)(x-3)=0\] \[x=-2,x=3\]

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